The volume of a cube is numerically equal to four times the sum of the lengths of its edges. What is the volume, in cubic units, of the cube? Express your answer in simplest radical

Guest Jul 18, 2022

#1**0 **

12sqrt(3) 12*edge*4=x^3 the area so the edge or x=4sqrt(3) 4sqrt(3)^3=area so it is 12sqrt(3)

MathBreathing Jul 18, 2022

#2**+1 **

the lentgh of all edges is 12 and sqrt(12) is 2sqrt(3)

SO THE ANSWER IS 2sqrt(3)

pogfrog123456789 Jul 18, 2022

#6**0 **

Let the side of the cube be \(s\). We have the equation \(s^3 = 4 \times 12s\)

Solving the equation gives us \(s = \sqrt{48} = 4 \sqrt{3}\)

So, the volume of this is \((4 \sqrt 3)^3 = \color{brown}\boxed{192 \sqrt 3}\)

BuilderBoi Jul 18, 2022